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Far-UV and near-UV fluxes of 46 bright HII regions in M81 are obtained from images acquired by the Ultraviolet Imaging Telescope (UIT) during the December 1990 Astro-1 Spacelab mission. Optical fluxes are obtained in the V band from a ground-based CCD image. Extinctions are estimated by comparing the observed $m_{249}-V$ colors with $-3.0$, the color of a model spectrum for clusters of age less than 3 Myr. The Galactic extinction curve (Savage and Mathis 1979) then determines the optical extinction for each HII region. A spectrum modeling program using the stellar evolution calculations of Schaller \ea (1992), the model atmospheres of Kurucz (1992), and the UIT filter curves determines the time variation of the ratio of the Lyman continuum luminosity to the far-UV luminosity. Calulations are performed for IMFs with slope $-1$, $-1.5$, and $-2$ (Salpeter=$-1.35$), and for stellar upper mass limits $120, 85, 60$, and $40$ \msol. The calculations suggest that for clusters of age less than $2$ Myr, $log(N_{Lyc}/L_{fuv})\sim 13.6,$ with scatter $0.2$. Lyman continuum fluxes for the observed HII regions are determined using the \ha fluxes of Petit et al. (1988). Values of $log N_{Lyc}/L_{fuv}$ computed using dereddened UV and \ha fluxes are in the range $\sim 11-13.$ Extinction of the Lyman continuum within the HII regions is not accounted for in these calculations. A plot of $log N_{Lyc}/L_{fuv}$ vs. $A_{V}$ gives an approximately linear relation,suggesting that a nearly constant fraction of the extinction determined from the $m_{249}-V$ color takes place within the HII region. If a fraction x of the extinction takes place within the HII region, then $A_{912}/E(B-V)=5.77/x$. Another effect which could decrease $N_{Lyc}/L_{fuv}$ below the value computed for very young clusters is star formation over an extended period of time, with a decreasing rate. The observed relation between $log N_{Lyc}/L_{fuv}$ and $A_{V}$ could be partially explained by such a model.
